We want to study the characteristics and the physical extent of the old populations in a sample of Local Group galaxies in different environments, from the dSph satellites in the halo of M31 to the isolated dIrr galaxies and to the haloes of M31 and M33 themselves. For this purpose, we plan to adopt RR Lyraes as stellar tracers. We need to obtain a complete census of these stars in the galaxies (or field of each galaxy) under study to construct high quality light-curves of the variable stars, to determine their distribution of periods, and the fraction of RRab, RRc, and multimode RRd variables. An important by-product of these observations will be very deep color-magnitude diagrams covering, in the case of the dwarf galaxies, most of each galaxy's field. This will provide an independent constraint on the star formation history of each galaxy.